What is a trademark?

Simply put, it's a brand name. More formally, it's "a word, phrase, symbol or design, or a combination of words, phrases, symbols or designs, that identifies and distinguishes the source of the goods of one party from those of others." (USPTO) A service mark identifies a service rather than a product.

Trademark protection only applies to a particular category of goods or services, although a single trademark owner may use it in multiple categories. For example, Nike Inc. owns the mark on a variety of shoes, clothing, sporting goods, etc., but Sweden's Nike Corporation could not prevent their use of the name because Nike Corporation's trademark was for heavy machinery, including hydraulic lifting jacks, pistons and presses.